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He seems to mean it light-heartedly. A little later he writes,

We are all Platonists, aren’t we? In the trenches, I mean—when the chips are down. Yes, Virginia, there really are circles, triangles, numbers, continuous functions, and all the rest. Well, maybe not free ultrafilters. Is it important to believe in the existence of free ultrafilters? Surely that’s not required of a Platonist. I can more easily imagine it as a test of sanity: “He believes in free ultrafilters, but he seems harmless.”